Introduction

In structural systems, many members are designed to resist forces applied laterally or transversely to their longitudinal axis. These members are referred to as beams. Common examples include:

• Axles in automotive systems
• Shafts in rotating machinery
• Structural elements in bridges and buildings

Beams may be subjected to the following types of loads:

• Axial Force — along the length of the beam
• Shear Force — perpendicular to the axis, causing sliding between layers
• Bending Moment — causing the beam to bend or flex

Beam Cross-Sections

Beams can have various cross-sectional shapes depending on design requirements. These include:

• Rectangular
• Circular
• I-section (I-beam)
• T-section
• Channel section

Figure 2.14 illustrates these cross-sectional profiles, which influence the beam’s strength, stiffness, and resistance to bending and shear.

Loading Effects

When a beam is loaded transversely, internal forces develop to maintain equilibrium. These include:

• Shear Force (V): Varies along the length and causes vertical displacement between layers.
• Bending Moment (M): Causes curvature in the beam, with maximum values typically at fixed supports or mid-span.

These internal forces are functions of the external loading and support conditions, and are typically represented using Shear Force Diagrams (SFD) and Bending Moment Diagrams (BMD).